While looking at sunspot information in connection with Amateur Radio, I found that the Sun rotates on a period from 27 days to 31 days. Its rotation is differential, at the equator it spins at a rate of about 27 days, while at the poles it's closer to 31 days.

Earth's moon also rotates at a rate of 27.3 days.

I suspect this is nothing more than coincidence, but was wondering if there is more than a coincidental connection between these two rates of rotation, similar to how tidal locking forces the moon's rotation and orbit around earth to be the same rate.

3 Answers
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Why? Because the moon used to rotate faster and is continually slowing down. Long story short, you just happen to be at a point in history where they two numbers roughly coincide. A few million years ago it wasn't true, and a few million years from now it wont be either.

And just to cover all my bases, there's nothing to suggest that the slowing orbit of the moon can have any reciprocal effect on the sun's rotational period.

Rotation of these object is caused by conservation of angular momentum. So while the rotation of the moon has changed as it became tidally locked with Earth, the total angular momentum of the Earth-moon system hasn't. So it could affect it but given the rotation periods of planets (http://en.wikipedia.org/wiki/Rotation_period) this is just a coincidence.